#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>

namespace IO {
    template <typename _T>
    inline bool read (_T& x) {
        x = 0;
        _T y = 1;
        char c = getchar();
        while ((c < '0' || '9' < c) && c != EOF) {
            if (c == '-') y = -1;
            c = getchar();
        }
        if (c == EOF) return false;
        while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getchar();
        x *= y;
        return true;
    }

    template <typename _T>
    inline _T input () {
        _T x = 0, y = 1;
        char c = getchar();
        while ((c < '0' || '9' < c) && c != EOF) {
            if (c == '-') y = -1;
            c = getchar();
        }
        if (c == EOF) return 0;
        while ('0' <= c && c <= '9') x = x * 10 + c - '0', c = getchar();
        x *= y;
        return x;
    }
};
using namespace IO;

#define reg register
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define rep(i, l, r) for(int i = l; i <= r; ++i)
#define lep(i, l, r) for(int i = l; i < r; ++i)
#define irep(i, r, l) for(int i = r; i >= l; --i)
#define ilep(i, r, l) for(int i = r; i > l; --i)
typedef long long ll;

int main () {
#ifdef LOCAL
#endif
    return 0;
}
